A torsional vibration damping disk having receiving spaces for bow spring elements, which are each arranged between two limit stop areas in the peripheral direction is known from U.S. Pat. No. 6,675,457. In the production of the known torsional vibration damping disk, the spring elements are inserted into the preformed receiving spaces. After the insertion of the spring elements, the sheet metal material delimiting the receiving spaces is further deformed around the spring elements in a manner that prevents the spring elements from falling out of the receiving spaces.